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1

Wykorzystanie modeli regresji składowych głównych w badaniu zjawisk społeczno-ekonomicznych

100%
Katarzyna Maruszewska K.
Zeszyty Naukowe Wyższej Szkoły Bankowej we Wrocławiu
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2013
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issue 2(34)
307-325
PL
Metoda głównych składowych podobnie jak analiza czynnikowa jest jedną z metod eksploracyjnych, które koncentrują się na badaniu powiązań w zbiorze danych. Polega ona na przekształceniu zbioru skorelowanych zmiennych w nowy zbiór składowych ortogonalnych, będących kombinacjami liniowymi zmiennych pierwotnych. Metoda ta jest szczególnie przydatna w analizie obszernych zbiorów danych; umożliwia redukcję wymiaru analizy oraz eliminację współliniowości zmiennych bez znaczącej utraty informacji pierwotnych. W artykule przedstawiono przykłady zastosowania modeli regresji składowych głównych w badaniu demograficznych, społecznych i ekonomicznych uwarunkowań przestrzennego zróżnicowania emigracji z Polski.
EN
Principal Component Analysis is a linear dimensionality reduction technique, which identifies orthogonal directions of maximum variance in the original data, and projects the data into a lower-dimensionality space formed from a sub-set of the highest-variance components. Principal components may be used as independent variables in regression models – the method is useful as there is a significant correlation of input data. The paper presents Principal Component Regression (PCR) as a method for identifying the factors which influence migration decisions on macro level in Poland and for analyzing its spatial differentiation.
2
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The dimensions of national competitiveness: The empirical analysis based on The World Economic Forum’s data

100%
Adamkiewicz H. G.
Economics and Business Review
|
2019
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vol. 5 (19)
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issue 3
EN
The aim of this research is to determine the minimum number of uncorrelated dimensions which can describe national competitiveness (NC). NC is thought of as the ability of a nation to provide a conducive environment for its firms to prosper. It is shown that the environment affects national productivity catalytically through the interactions with the production factors while itself remaining unchanged. Selected World Economic Forum’s indicators are used for determining the components of the environment. The Principal Component Analysis has revealed three orthogonal dimensions of NC. Countries are represented by the points in the three-dimensional space. The weighted Euclidean distance from the origin to the ith point is proposed as a novel measure of the ith country’s level of NC.
3
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A comparative analysis of the principal component method and parallel analysis in working with official statistical data

75%
Holubova H.
Statistics in Transition new series
|
2023
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vol. 24
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issue 1
199-212
EN
The dynamic development of the digitized society generates large-scale information data flows. Therefore, data need to be compressed in a way allowing its content to remain complete and informative. In order for the above to be achieved, it is advisable to use the principal component method whose main task is to reduce the dimension of multidimensional space with a minimal loss of information. The article describes the basic conceptual approaches to the definition of principle components. Moreover, the methodological principles of selecting the main components are presented. Among the many ways to select principle components, the easiest way is selecting the first k-number of components with the largest eigenvalues or to determine the percentage of the total variance explained by each component. Many statistical data packages often use the Kaiser method for this purpose. However, this method fails to take into account the fact that when dealing with random data (noise), it is possible to identify components with eigenvalues greater than one, or in other words, to select redundant components. We conclude that when selecting the main components, the classical mechanisms should be used with caution. The Parallel analysis method uses multiple data simulations to overcome the problem of random errors. This method assumes that the components of real data must have greater eigenvalues than the parallel components derived from simulated data which have the same sample size and design, variance and number of variables. A comparative analysis of the eigenvalues was performed by means of two methods: the Kaiser criterion and the parallel Horn analysis on the example of several data sets. The study shows that the method of parallel analysis produces more valid results with actual data sets. We believe that the main advantage of Parallel analysis is its ability to model the process of selecting the required number of main components by determining the point at which they cannot be distinguished from those generated by simulated noise.
4
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Factorization methods applied to characterize the sources of volatile organic compounds in Montreal, Quebec

75%
Porada E., Kousha T.
International Journal of Occupational Medicine and Environmental Health
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2015
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vol. 29
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issue 1
15-39
EN
Objectives The study objective was to assemble emission characteristics of the sources of the ambient volatile organic compounds (VOCs) and to elaborate methods of organizing them into the sources’ chemical profiles. Material and Methods The UNMIX – sensor modeling method from the U.S. Environment Protection Agency (EPA) – was used to process the VOC concentration data acquired over the years 2000–2009 for 175 VOC species in 4 air quality monitoring stations in Montreal, Quebec. Results The method enabled to assess VOC emissions from the typically distributed sources existing in urban environment and VOC occurrences characterizing the local, or point-like, sources. The distributed sources were inextricably associated with hydrocarbons from exhaust, heavier hydrocarbons from contaminated urban soil, fugitive evaporations of gasoline and liquefied petroleum gases (LPG), leakage from the industrial and commercial use of solvents, and the inert, ozone depleting gases permeating urban atmosphere. The sources’ profiles were charted involving 60–120 VOC species per source. Spatial distribution of the sources was examined. Conclusions The UNMIX application and the source profiling methods, by building robust chemical profiles of VOC sources, provided information that can be used to assign the measured VOC emissions to physical sources. This, in turn, provides means of assessing the impact of environmental policies, on one hand, and of industrial activities on the other hand on VOC air pollution.
5

Principal component analysis for authorship attribution

63%
Jamak A., Savatić A., Can M.
Business Systems Research Journal
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2012
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vol. 3
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issue 2
49-56
EN
Background: To recognize the authors of the texts by the use of statistical tools, one first needs to decide about the features to be used as author characteristics, and then extract these features from texts. The features extracted from texts are mostly the counts of so called function words. Objectives: The data extracted are processed further to compress as a data with less number of features, such a way that the compressed data still has the power of effective discriminators. In this case feature space has less dimensionality then the text itself. Methods/Approach: In this paper, the data collected by counting words and characters in around a thousand paragraphs of each sample book, underwent a principal component analysis performed using neural networks. Once the analysis was complete, the first of the principal components is used to distinguish the books authored by a certain author. Results: The achieved results show that every author leaves a unique signature in written text that can be discovered by analyzing counts of short words per paragraph. Conclusions: In this article we have demonstrated that based on analyzing counts of short words per paragraph authorship could be traced using principal component analysis. Methodology could be used for other purposes, like fraud detection in auditing.
6
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Zastosowanie metod wielowymiarowej analizy porównawczej do oceny stanu środowiska w województwie dolnośląskim

51%
Bąk A.
Wiadomości Statystyczne. The Polish Statistician
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2018
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issue 1
7-20
EN
The aim of this article is to present the results of multidimensional comparative analysis methods used to assess the state of the environment in Dolnośląskie voivodship in the cross-section of powiats. The research was conducted on the basis of data from the CSO of Poland for 2015 concerning the state and environmental protection in 30 powiats of Dolnośląskie voivodship. The method of linear ordering of objects based on a pattern object (or an anti-pattern object) was used in the research. Many of them described in the subject literature usually lead to differing results (rankings of objects are not the same). It results from i.a. the adopted methods of normalization and weighing of variables and aggregations (creation of synthetic variables). The article is an attempt to compare the results of linear ordering of powiats due the environmental state with the use of method based on a pattern object (or an anti-pattern object). In the rankings correctness analysis, quality indicators were used to evaluate the quality of linear ordering methods.
PL
Celem opracowania jest zaprezentowanie wyników metod wielowymiarowej analizy porównawczej wykorzystywanej do oceny stanu środowiska w województwie dolnośląskim w przekroju powiatów. Badanie przeprowadzono na podstawie danych GUS za 2015 r. dotyczących stanu i ochrony środowiska w 30 powiatach województwa dolnośląskiego. W badaniu zastosowano metody porządkowania liniowego obiektów (wzorcowe i bezwzorcowe). Wiele z nich opisanych w literaturze przedmiotu na ogół prowadzi do zróżnicowanych wyników (rankingi obiektów nie są takie same). Wynika to m.in. z przyjętych metod normalizacji i ważenia zmiennych oraz agregacji (tworzenia zmiennych syntetycznych). W artykule podjęto próbę porównania wyników porządkowania liniowego powiatów ze względu na stan środowiska za pomocą wybranych metod wzorcowych i bezwzorcowych. W analizie poprawności rankingów wykorzystano mierniki oceny jakości metod porządkowania liniowego.
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